Answers
Answer:
a) decay
b) 2,950,000
c) 0.025
d) [tex]f(x)=2950000(0.975)^x[/tex]
e) 2,409,123
Step-by-step explanation:
Part (a)
Exponential DECAY, since the population was decreasing annually.
Part (b)
Initial amount = 2,950,000 people (in the year 2000)
Part (c)
Decay factor = 2.5% = 0.025 (in decimal form)
Part (d)
General form of exponential decay function:
[tex]f(x)=a(1-r)^x[/tex]
where:
a = initial amountr = rate of decay (in decimal form)x = time (in years)Given:
a = 2950000r = 0.025[tex]\implies f(x)=2950000(1-0.025)^x[/tex]
[tex]\implies f(x)=2950000(0.975)^x[/tex]
Part (e)
To determine the city's population in 2008:
[tex]x = 2008 - 2000 = 8[/tex]
[tex]\begin{aligned}\implies f(8) & =2950000(0.975)^8\\ & = 2409123\: \sf(nearest\:whole\:number)\end{aligned}[/tex]
Related Questions
What is the equation of a line in general form that does not have a y-intercept and goes through the point (3,6) ?
(** I know the answer is x-3 = 0, please EXPLAIN)
Answers
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
Step 1: Determine the equation
So we know that our equation does not have a y-intercept which means that it doesn't intersect ANYWHERE on the y-axis. Therefore, this means that our equation will be a straight vertical line that doesn't move side to side and just goes straight up and down. We also know that our point is (3, 6) which means that our x-value will be 3 and this is where the equation will be located.
There are several ways to display our answer where x = 3 is the most common way which basically means give me all of the y-values for the same x value of 3. Another way of saying it is x - 3 = 0 which either way when adding 3 to both sides gives you x = 3 which is what I usually go with.
Answer: [tex]x = 3[/tex]
Answer:
x = 3 or x - 3 = 0
Step-by-step explanation:
Given
It does not have a y-interceptPasses through the point (3, 6)Solving
If the line cannot touch the y-axis, it has to be parallel to it (in other words, the line must be vertical)Since the x-value is constant for a vertical line and it passes through the point (3, 6), the equation of the line will be :x = 3 or x - 3 = 0What is the value of the remainder?
Answers
[tex] \underline{ \boxed{ \sf{✰\: Option\:D. \:81✓ }}}[/tex]
Refer to the attachment for solution ☘️
Hope it helps
Please help, thank you!
Answers
Answer:
Vertical Asympote, but I might be wrong, haven't done this math in years
Kate packs snow into 5 identical jars. each jar represents a different depth of snow. kate then lets the snow in each jar completely melt. the table shows the height of the liquid in each jar as it relates to the original depth of snow in the jar. a 2-column table with 5 rows. the first column is labeled snow depth (inches), x with entries 2, 4, 6, 8, 10. the second column is labeled water depth (inches), f(x) with entries 0.4, 0.8, 1.2, 1.6, 2.0. which statements are true about the relationship between the depth of the snow and the height of water in the jar after the snow is melted? select two options. the points on a graph representing the relationship lie on a line. there is 0.4 inch of water to every 1 inch of snow. a line through the points will pass through (0, 0). the function relating snow depth to water depth is quadratic. the data can be represented by f(x) = 0.2x.
Answers
The true statements include the point on the graph represents the relationship lie on a line and a line through the points will pass through (0, 0).
How to illustrate the table?From the table, the water depth changes for about (0.8 - 0.4) = 0.4 inches. Here, the function is a linear model.
In this case, the the point on the graph represents the relationship lie on a line and a line through the points will pass through (0, 0).
Learn more about graphs on:
https://brainly.com/question/19040584
Answer:
A & C
Step-by-step explanation:
hope this helps
Which absolute value inequality is modeled by this graph?
A. y ≥ |x − 3|
B. y ≥ |x| − 3
C. y > |x + 3|
D. y > |x| + 3
Answers
Answer:
c
Step-by-step explanation:
sorry if it is wrong
Just plug in 0 and you have to get -3 because there is a point (0,-3)
A: you get |0-3| = |-3| = 3. Not A.
B: you get |0| -3 = -3. Correct
C: you get |0+3| =|3|=3. Not C
D: you get |0| +3 =3 Not D
Find the least common denominator of 11/10 and 1/15
Answers
Answer: The least common denominator is 30.
Step-by-step explanation: Look at the image I have uploaded.
Good luck!
Twenty-one less than a number is seven. What is the number? 3 14 28 147
Answers
Answer:
Option C, 28
Step-by-step explanation:
Step 1: Make an expression
Twenty-one less than a number is 7
[tex]x - 21 = 7[/tex]
Step 2: Solve the equation for x
[tex]x - 21 = 7[/tex]
[tex]x - 21 + 21 = 7 + 21[/tex]
[tex]x = 28[/tex]
Answer: Option C, 28
Answer:
28
Step-by-step explanation:
because twenty eight subtracted by twenty one equals seven
Which side is opposite angle C?
None
BC
AB
AC
Answers
Answer:
AB
Step-by-step explanation:
opposite is AB
Bob sells part of a 50-acre rectangular plot of land he owns so that he can still own a smaller rectangular plot within the original. After he makes the sale, Bob's remaining plot of land is half as long and half as wide as his original plot. What is the area of Bob's remaining plot of land?
Answers
Considering the area of a rectangle, it is found that the area of Bob's remaining plot of land is of 12.5 acres.
What is the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, that is:
A = lw.
In this problem, both the length and the width are divided in half, hence the proportion remaining is given by:
A = 0.5l x 0.5w = 0.25lw = 25% of the initial area.
Hence:
0.25 x 50 = 12.5.
The area of Bob's remaining plot of land is of 12.5 acres.
More can be learned about the area of a rectangle at https://brainly.com/question/10489198
#SPJ1
The sum of a number x and 2,496 is 17,344. What is the value of x?
Answers
x = 17,344 - 2,496
x = 14,848
Multiplying by 1.19 is the same as increasing by
Answers
1.19 - 19%
Answer number 14 please. Thank you.
Answers
Answer:
i already did i the previous one
btw can you send this full page of work in pdf if you could
15.
[tex] \frac{89.32}{48.50} \times 100[/tex]
what is area of the polygon
Answers
hii ,
area of polygon : 18
What is the volume of the prism if its 2 centimeters long tall 12 centimeters wide and 25 centimeters long
Answers
Answer:
600 cm
Step-by-step explanation:
L*W*H SO IT WILL BE 2*12*25
Tran has a credit card with a spending limit of $2000 and an apr (annual percentage rate) of 12%. during the first month, tran charged $450 and paid $150 of that in his billing cycle. which expression will find the amount of interest tran will be charged after the first month? (0.01) (300 dollars) (0.01) (450 dollars) (0.12) (300 dollars) (0.12) (450 dollars)
Answers
The expression that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).
ExpressionFirst step
Monthly interest rate = (Annual percentage rate ÷ Number of months in a year)
Monthly interest rate= 0.12 ÷ 12
Monthly interest rate= 0.01
Second step
Amount left = Amount charged - Amount paid
Amount left = $450 - $150
Amount left = $300
Third step
Amount of interest=Monthly rate ×Amount left
Amount of interest=(0.01) (300 dollars)
Amount of interest=$3
Therefore the expression that will find the amount of interest tran will be charged after the first month is: (0.01) (300 dollars).
Learn more about expression here:https://brainly.com/question/11277823
If 6 pairs of socks cost $6. 90, what is the price for one pair of socks
Answers
Answer:
$1.15
Step-by-step explanation:
6 pairs of socks cost $6.90.
so every sock is at least one dollar. one dollar per sock, then you take the .90 and divided between the 6 socks and you get 15, so one dollar and 15 cents per sock.
Hope this helps, have a nice day!
PLEASE HELP
i have no clue what im doing wrong but i cannot find the answer
Answers
Please Help !! What is the surface area of a cylinder with base radius 4 and height 5. Show your work .
Answers
Answer:
226.19
Step-by-step explanation:
A= 2πrh+ 2πr2= 2·π·4·5+2·π·42≈226.19467
or
S = (2 * pi * r^2) + (2 * pi * r * h)
S = (2 * pi * 4^2) + (2 * pi * 4 * 5)
S = (32 pi) + (40 pi) = 72pi = 226.08 ANS.
Answer:
251.333 (Repeating)
Step-by-step explanation:
First, you need to find the area of the circle at the top, which is [tex]\pi r^{2}[/tex]
Next, you multiply it by the height. (I did also use actual pi)
This is if it's total area, not lateral.
hello what is 5x6 and what is 24 divide by 50
Answers
Answer:
5×6=30
24÷50=0.49....following long division method
Dale wants to order business cards for his new job.
• Company A charges a flat fee of $0.15 per card.
• Company B charges $0.10 per card plus an additional $10.00 for delivery
Write an inequality for the amount of business cards, c, that Dale would need to buy for Company to be cheaper
Answers
Dale would need to buy more than 200 cards for Company B to be cheaper.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Company A charges a flat fee of $0.15 per card.
Company B charges $0.10 per card plus an additional $10.00 for delivery
Let x = number of cards
Company A charges = $0.15x
Company B charges = $10.00 + $0.10x
For company B to be the cheaper option ( B < A )
$10.00 + $0.10x < $0.15x
$10.00 < $0.05x
subtracting positive from both sides to retains the sense of the inequality and x is positive
200 < x
x > 200
So, Dale would need to buy more than 200 cards for Company B to be cheaper.
Learn more about inequality ;
https://brainly.com/question/10867023
#SPJ1
HELP please this is due soon
Answers
Answer:
Step-by-step explanation:
Side Opposite to ∠x is called YZ
The side Opposite to ∠y is called XZ (that's the hypotenuse of the triangle)
Side Opposite to ∠Z is XY
Answer:
Side apposite to angle X is YZ
Side apposite to angle Y is XZ
Side apposite to angle Z is XY
Hope this helps you
have a great day
Hey I kinda need some help with this could u help?
Answers
Answer:
[tex]x = 13 ~~ \text{and}~~ y= 10[/tex]
Step-by-step explanation:
[tex]~~~~~~2.31 \times 10^x = 2200 \times 1.05 \times 10^y\\\\\implies 2.31 \times 10^x = 2310 \times 10^y\\\\\implies \dfrac{10^x}{10^y} = \dfrac{2310}{2.31}\\\\\implies 10^{x-y}=1000\\\\\implies 10^{x-y} = 10^3\\\\\implies x - y = 3[/tex]
[tex]\text{If x = 13 and y = 10 then the difference will be 3.}[/tex]
A door's shape is made by combining a rectangle and a semicircle. What is the area of the door?
Answers
Answer:
34.28 ft²Step-by-step explanation:
Area of the door = area of the rectangle + area of the semicircle
= 7 × 4 + (3.14 × 2²)/2
= 28 + (3.14 × 4)/2
= 28 + 3.14 × 2
= 28 + 6.28
= 34.28
A train travels from Washington D.C. to New York (225 miles). The train departs at 4:55 PM and arrives in New York at 7:55 PM. What is the average speed of the train?
Answers
7:55 pm - 4:55 pm = 3 hours
225 miles / 3 hours = 75 miles per hour
Average speed = 75 miles per hour
find the measure of the missing angle?
Answers
56+72+x =180 ( therefore sum of angle in a triangle)
128+x=180
x=180-128
x=52
Answer:
THE MISSING ANGLE = 52°
Step-by-step explanation:
Sum of all angles = 18°0
Let the missing angle be x°
56° + 72° + x° = 180°
x° = 180° - 72° - 56°
x° = 52°
!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
A bag contains 3red, 4white, 5green balls. Three balls are selected without replacement. Find the probability that the three balls chosen are:
A) all red
B) all green
C)one of each color
Answers
Answer:
A. 1/220 B. 1/22 C. 3/11
Step-by-step explanation:
This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).
Notations for combinations:
The number of ways to select r things from a set of n things is
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex] where the exclamation points mean factorial.
[tex]n!=1\cdot2\cdot3\ldots\cdot n[/tex] and 0! is defined to be 1.
There are two other commonly used symbols for this:
[tex]_nC_r[/tex] and [tex]n \choose x[/tex].
In all three parts, the number of ways to choose 3 balls from a set of 12 is
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}[/tex]
Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220[/tex]
A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.
B) The number of ways to choose 3 green balls from the set of 5 green balls is [tex]C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10[/tex] out of 220, so the probability is 10/220 = 1/22.
C) The number of ways to choose 1 red is C(3, 1) = 3. Choose 1 green in C(5, 1) = 5 ways. Choose 1 white in C(4, 1) = 4 ways.
The probability is [tex]\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}[/tex]
Answer:
a) 1/220
b) 1/22
c) 3/11
Step-by-step explanation:
Check the attachment.
what is the solution for the equation -15=5(3y-10)-5y
Answers
Answer:
[tex]\Large\boxed{\sf{y=\dfrac{7}{2} }}[/tex]Step-by-step explanation:
Isolate the variable of y from one side of the equation.
-14=5(3y-10)-5y
First, switch sides.
[tex]\sf{5\left(3y-10\right)-5y=-15}[/tex]
Use the distributive property.
DISTRIBUTIVE PROPERTY:
A(B-C)=AB-AC
5(3y-10)
Multiply by expand.
5*3y=15y
5*10=50
15y-50-5y
15y-5=10y
= 10y-50
10y-50=-15
Add by 50 from both sides.
10y-50+50=-15+50
Solve.
10y=35
Then, you divide by 10 from both sides.
10y/10=35/10
Solve.
Divide the numbers from left to right.
35/10=7/2
y=7/2
Divide is another option.
7/2=3.5
[tex]\Longrightarrow: \boxed{\sf{y=\dfrac{7}{2}}}[/tex]
Therefore, the correct answer is y=7/2.I hope this helps. Let me know if you have any questions.
what are the mean,median,mode, and range of the data set given the altitude of lakes in feet:-11,-28,-17,-25,-28,-39,-6,and -46? i dont know the answer
Answers
Answer:
Read explanation.
Step-by-step explanation:
The average is -22.2 (mean)
-46,-39,-28,-28,-25,-17,-11.-6 You cross out the lowest and highest until you reach the middle, which is -26.5(median)
The mode is -28 as it is the most repeated number
The range is 40 as when you subtract a negative it turns into the absolute value.
please help im sorry i dont understand shapes and angles
Answers
Answer:
Sorry I can't answer this.
But you may use the protacter to find the angle
? = 73°
There are 7 sides in this polygon
Calculate total interior angles using (n-2) * 180
["n" denotes number of sides]
Here total interior angle: (7-2)*180 = 900°The missing angle inside the polygon:
900° - 130° -119° -130° -154° -130° -130°
900° - 793°
107°
A straight line has total 180°
? + 107° = 180°
? = 180° - 107°
? = 73°
PLS HELPP WHAT IS THE ANSWER???
Answers
Answer:
-220
Step-by-step explanation:
Answer:
Let us start by plugging in x=2 into all variables x and y=1 into all y's
so: The result is -220